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From Quantum Curves to Topological String Partition Functions II.

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This summary is machine-generated.

This study geometrically characterizes topological string partition functions using quantum curves derived from Calabi-Yau manifolds. These functions correspond to Exact WKB coordinates, revealing insights into supersymmetric field theories.

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Area of Science:

  • String Theory
  • Mathematical Physics
  • Supersymmetric Field Theories

Background:

  • Topological string theory and Calabi-Yau (CY) manifolds are crucial for geometric engineering of d=4, N=2 supersymmetric field theories of class S.
  • Quantum curves, derived from quantizing CY manifolds, are differential operators central to this study.

Purpose of the Study:

  • To provide a geometric characterization of topological string partition functions.
  • To establish a connection between these partition functions and preferred coordinates on quantum curve moduli spaces.

Main Methods:

  • Geometric characterization of topological string partition functions.
  • Extraction of partition functions from isomonodromic tau-functions via generalized theta series expansions.
  • Definition of preferred coordinates using the Exact WKB method.

Main Results:

  • A one-to-one correspondence was found between topological string partition functions and preferred coordinates on quantum curve moduli spaces.
  • These preferred coordinates exhibit jumps across specific loci in the moduli space.
  • The normalization changes of tau-functions associated with these jumps define a natural line bundle.

Conclusions:

  • The proposed geometric characterization offers a novel framework for understanding topological string partition functions.
  • The identified line bundle plays a pivotal role in this geometric framework.
  • This work bridges concepts from string theory, quantum curves, and the Exact WKB method.